Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
348 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#4097 | C2 | semidirect |
| 3. C5×#4055 | C2 | semidirect |
| 4. C5×#4021 | C2 | semidirect |
| 5. C52×#104 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. C5×#3937 | C2 | semidirect |
| 16. C2×C5×Dic10 | C22 | semidirect |
| 17. C52×M16 | C22 | semidirect |
| 18. C42×C52 | C22 | semidirect |
| 22. C5×#681 | C22 | semidirect |
| 26. #65114 | C5 | direct (N × H) |
| 54. #4097 | C2×C5 | semidirect |
| 55. #4055 | C2×C5 | semidirect |
| 56. #4021 | C2×C5 | semidirect |
| 59. C5×#104 | D5 | semidirect |
| 60. C5×#104 | C2×C5 | semidirect |
| 62. #3955 | C2×C5 | semidirect |
| 63. #3937 | C2×C5 | semidirect |
| 94. C2×Dic10 | C22×C5 | semidirect |
| 101. C5×M16 | C2×D5 | semidirect |
| 102. C5×M16 | C22×C5 | semidirect |
| 105. C42×C5 | C2×D5 | semidirect |
| 106. C42×C5 | C22×C5 | semidirect |
| 110. #681 | C22×C5 | semidirect |
| 175. #104 | C5×D5 | semidirect |
| 177. C52 | #455 | semidirect |
| 222. M16 | C2×C5×D5 | semidirect |
| 224. C42 | C2×C5×D5 | semidirect |
| 261. C5 | #65114 | direct (N × H) |
| 262. C5 | C5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4149 | 2 |
| C5×#4097 | 2 |
| C5×#4055 | 2 |
| C5×#4021 | 2 |
| C52×#104 | 2 |
| C5×#3955 | 2 |
| C5×#3937 | 2 |
| C5×#455 | 5 |
| #65114 | 5 |